Please humour an economist coming here in peace! I am trying to track down the classic textbook definition of a causal system. I know it is a system which only depends on current and previous input values but it would be nice to know what is THE reference for this. I was browsing through past messages on this board and it seems that people may be able to help. Thanks very much in advance.
Textbook definition of causal
Started by ●October 13, 2009
Reply by ●October 13, 20092009-10-13
On 13 Okt, 14:41, "italrosso" <martin.elli...@economics.ox.ac.uk> wrote:> Please humour an economist coming here in peace! > > I am trying to track down the classic textbook definition of a causal > system. I know it is a system which only depends on current and previous > input values but it would be nice to know what is THE reference for this. > > I was browsing through past messages on this board and it seems that > people may be able to help. > > Thanks very much in advance.The wikipedia page lists Aristotle among the sources: http://en.wikipedia.org/wiki/Causality_(physics) It would presumably be hard to find any earlier than that... Rune
Reply by ●October 13, 20092009-10-13
Reply by ●October 13, 20092009-10-13
On Tue, 13 Oct 2009 07:41:44 -0500, italrosso wrote:> Please humour an economist coming here in peace! > > I am trying to track down the classic textbook definition of a causal > system. I know it is a system which only depends on current and previous > input values but it would be nice to know what is THE reference for > this. > > I was browsing through past messages on this board and it seems that > people may be able to help. > > Thanks very much in advance.I think you may be trying to gild the lily -- your definition is perfectly good as it stands. You will find authors that don't consider a system to really be causal unless the output is strictly after the input, as opposed to after or at the same time -- so you have to be careful in your use and interpretation of the term as you go through the literature. If there's any reason to fuss over causal systems it's because it is so easy to write down equations for an acausal system, and if you are describing a system in the frequency domain it may not be "slap me upside the head" obvious that you've done so. -- www.wescottdesign.com
Reply by ●October 13, 20092009-10-13
On 10/13/2009 9:01 AM, Tim Wescott wrote:> On Tue, 13 Oct 2009 07:41:44 -0500, italrosso wrote: > >> Please humour an economist coming here in peace! >> >> I am trying to track down the classic textbook definition of a causal >> system. I know it is a system which only depends on current and previous >> input values but it would be nice to know what is THE reference for >> this. >> >> I was browsing through past messages on this board and it seems that >> people may be able to help. >> >> Thanks very much in advance. > > I think you may be trying to gild the lily -- your definition is > perfectly good as it stands. You will find authors that don't consider a > system to really be causal unless the output is strictly after the input, > as opposed to after or at the same time -- so you have to be careful in > your use and interpretation of the term as you go through the literature. > > If there's any reason to fuss over causal systems it's because it is so > easy to write down equations for an acausal system, and if you are > describing a system in the frequency domain it may not be "slap me upside > the head" obvious that you've done so. >I'm with Tim, you already know the definition as well as anyone. There are a lot of terms, like "causality", that get abused from time to time by people stretching the definition a little bit to help describe their system or perhaps to bring in certain techniques where they barely apply, or whatever. The result is that for definitions the case is often that when one moves from the general definition to a tighter one a lot fewer people agree on what it means. So when moving to a tighter definition one has to be careful that it applies in the context being used, and that one then doesn't drift out of that context, etc., etc. That's all a very long way to say that you have the general definition and unless you have a restricted context and a reason to use something more specific the general definition is about as good as it gets. I don't know if it's like that in economics or not, but DSP seems to be especially susceptible to this terminology problem. -- Eric Jacobsen Minister of Algorithms Abineau Communications http://www.abineau.com
Reply by ●October 13, 20092009-10-13
Thank you everyone for your comments. It is interesting that even in engineering it is hard to pin down precise definitions. I would have thought you guys would have found this much easier! Your help is very much appreciated.
Reply by ●October 13, 20092009-10-13
On Oct 13, 8:41 am, "italrosso" <martin.elli...@economics.ox.ac.uk> wrote:> Please humour an economist coming here in peace! > > I am trying to track down the classic textbook definition of a causal > system. I know it is a system which only depends on current and previous > input values but it would be nice to know what is THE reference for this. > > I was browsing through past messages on this board and it seems that > people may be able to help. > > Thanks very much in advance.I'm not sure about the level of detail you're looking for. Here's a partial stab: For discrete sytems (i.e. index is a countable set e.g. time in resolution of seconds), the following definition is fairly standard. The reference is a standard undergraduate DSP textbook. http://books.google.com/books?ei=PcbUSrrWOYvEywSBkJnlDQ&client=firefox-a&id=Y_ZSAAAAMAAJ&dq=digital+signal+processing+causal+system&q=causal+system#search_anchor Some hunting in Google books will probably find you the continuous version of the definition also. Dilip.
Reply by ●October 13, 20092009-10-13
Reply by ●October 13, 20092009-10-13
>Thank you everyone for your comments. It is interesting that even in >engineering it is hard to pin down precise definitions. I would have >thought you guys would have found this much easier! > >Your help is very much appreciated.One analogy is to say you're providing economic advice, but you can only advise based on past data points; you don't know the future (though you can guess...again, based on the past). Tim's definitions caveat can be brought into this analogy by distinguishing between whether your advice can depend on the EXACT present: if you have minute-by-minute updates, can you really give updated advice in a tiny fraction of that minute? You can see that it depends on how you define your sampled time, but ultimately, it's an intuitive concept: you can only guess at the future, not measure it. Ultimately, anything you can actually physically implement is causal by some definition (even if it involves people waiting a day for your prediction, it can't make use of data that was unavailable at the time you made the prediction). Of course, not all systems try to predict, but I figured that's why you're asking. You can also smooth "random" jumps in your data from the past, but you still can't use future data points to do it. Are you looking for a particular derived form, such as what a causal impulse response looks like?
Reply by ●October 13, 20092009-10-13
On Oct 13, 7:41�am, "italrosso" <martin.elli...@economics.ox.ac.uk> wrote:> Please humour an economist coming here in peace! > > I am trying to track down the classic textbook definition of a causal > system. I know it is a system which only depends on current and previous > input values but it would be nice to know what is THE reference for this. > > I was browsing through past messages on this board and it seems that > people may be able to help. > > Thanks very much in advance.Reference: "Continuous and Discrete Signals and System Analysis" by McGillem and Cooper "A causal (or physical, or nonanticipatory) system is one whose present response does not depend upon future values of the input". Now that you have the definition, I must add that noncausal systyems are frequently approximated using delays. Maurice Givens
